The La dilution of the Kondo lattice CeCoIn5 is studied. The scaling laws found for the magnetic susceptibility and the specific heat reveal two well-separated energy scales, corresponding to the single-impurity Kondo temperature T(K) and an intersite spin-liquid temperature T(*). The Ce-dilute alloy has the expected Fermi liquid ground state, while the specific heat and resistivity in the dense Kondo regime exhibit non-Fermi-liquid behavior, which scales with T(*). These observations indicate that the screening of the magnetic moments in the lattice involves antiferromagnetic intersite correlations with a larger energy scale in comparison with the Kondo impurity case.